To find out who started with more money in their account, we need to analyze both accounts according to the information given.
Step 1: Analyzing Jennifer's Account
Jennifer's bank account balance is modeled by the equation: \[ y = 12x + 45 \] where \( x \) is the number of weeks and \( y \) is the total balance.
To find out how much money Jennifer started with (when \( x = 0 \)), we substitute \( x = 0 \) in the equation:
\[ y = 12(0) + 45 \] \[ y = 0 + 45 \] \[ y = 45 \]
So, Jennifer started with $45.
Step 2: Analyzing William's Account
Now let's look at William's account from the given data:
- Week 0: Balance = 30
- Week 1: Balance = 44
- Week 2: Balance = 5 (This appears to be an error in the data as it indicates a withdrawal or mistake since the balance should generally increase)
- Week 3: Balance = 72
- Week 4: Balance = 86
From the table, the balance at Week 0 for William is $30.
Step 3: Comparing Initial Balances
Now we compare the initial balances of both accounts:
- Jennifer's initial balance: $45
- William's initial balance: $30
Conclusion
Jennifer started with more money in her account. To summarize the reasoning:
- We calculated Jennifer's initial balance using the equation \( y = 12x + 45 \) by substituting \( x = 0 \).
- William’s initial balance was taken directly from the provided data, which indicated $30.
Therefore, \( 45 > 30 \), which shows Jennifer started with more money.